Question

Rani reads a few pages of a novel every day. She reads the following number of pages per day in a week: $23,26,21,19,37,18,24$. (i) Find the mean number of pages read by her. (ii) Also, find the median.

Answer 1

Hint: In this question, we have to find the mean and the median. Thus, we will use the formula to get the solution. As we know, the mean is the average of the observations from the data. Also, the median is the middle number of the observations. Thus, to find the mean, we will use the average formula $\dfrac{\text{sum of observations}}{\text{total number of observations}}$ . Then, for finding the median, we will first calculate whether the number of observations is odd or even be equal to n. then, we will arrange the observation in ascending order. Thus we see that the number of observations is odd, thus we will use the formula $\dfrac{n+1}{2}$ . After the necessary calculations, we get the required answer to the solution.

Complete step by step solution:
According to the problem, we have to find the value of mean and the median from the number of pages per day Rani reads in a week.
The number of pages is $23,26,21,19,37,18,24$ -------- (1)
Thus, the total number of observations is equal to n, that is $n=7$ --- (2)
(i) Now, we will first find the mean of the observations using the formula $\dfrac{\text{sum of obervations}}{\text{total number of observations}}$. So, we will put the value of equation (1) and (2) in the formula, we get
$\begin{align}
  & mean=\dfrac{23+26+21+19+37+18+24}{n=7} \\
 & mean=\dfrac{168}{7} \\
\end{align}$
Thus, on further simplification, we get
$mean=24$
Therefore, the mean of the observations is 24.
(ii) For finding the median of the observations.
We see that from equation (2), the number of observations is equal to 7, which is an odd number. Thus, we will use the odd-median formula to get the solution.
Thus, the ascending order of the observations is $18,19,21,23,24,26,37$ ----- (3)
Now, the odd-median formula is $\dfrac{n+1}{2}$ . Thus, putting the value of equation (2) in the formula, we get
$\begin{align}
  & median={{\left( \dfrac{7+1}{2} \right)}^{th}}observation \\
 & median={{\left( \dfrac{8}{2} \right)}^{th}}observation \\
\end{align}$
On further simplification, we get
$median={{\left( 4 \right)}^{th}}observation$
Thus, the $4^{th}$ observation in equation (3) is 23, which implies
$median=23$

Therefore, the median from the given number of observations is equal to 23.

Note: While solving this problem, do mention the formula and the steps properly to avoid confusion and mathematical error. Always remember the definition of mean and the median to get an accurate answer.